Reduced critical Bellman-Harris branching processes for small populations

2018/09/13 by Wenming Hong, Hong, Wenming, Yao Ji +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1809.05029

14 pages

arxiv created 2018/09/14 · arxiv updated 2018/09/17

Abstract

Let \ Z(t), t≥ 0\ be a critical Bellman-Harris branching process with finite variance for the offspring size of particles. Assuming that 0<Z(t)≤ φ(t), where either φ(t)=o(t) as t→ ∞ or φ(t)=at, a>0, we study the structure of the process % \ Z(s,t),0≤ s≤ t\ , where Z(s,t) is the number of particles in the process at moment s in the initial process which either survive up to moment t or have a positive offspring number at this moment.

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